Entropy Model of FIRO-Based TRNGs With Differential Structure

A digital true random number generator (TRNG) based on Fibonacci ring oscillators (FIRO), which boasts high throughput and a high entropy rate, was introduced by Jovan Dj. Golic. However, establishing an entropy model for FIRO-based TRNGS (FIRO-TRNGs) remains a challenging problem. In this paper, we aim at establishing an effective entropy model for the FIRO-TRNGs. To this end: 1) we have confirmed with theoretical analysis and experimental results that the standard entropy model suitable for elementary oscillator-based TRNGs (EO-TRNG) is not effective for assessing the entropy of FIRO-TRNGs due to the effect of flicker noise, and then 2) based on the differential principle, and by incorporating the inherent chaotic characteristics of FIRO-TRNGs, we have proposed a self-sampling FIRO-TRNG and an entropy model for it, finally 3) for providing the design parameters required in the entropy model, we present a measurement circuit for the phase jitter of the FIRO-TRNGs and theoretically derived the conditions for selecting the parameters of the jitter measurement circuit. Experimental results indicate that if the sampling is performed using the sampling parameters provided by the entropy model, then the output sequence possesses sufficient entropy. Alternatively, given a lower bound of entropy, an upper bound for the sampled frequency can be derived by using the measured phase jitter.